# How do I determine if the alternating series #sum_(n=1)^oo(-1)^n/sqrt(3n+1)# is convergent?

Test for Alternating Series

Let's examine the alternating series that is posted.

and

Thus, using the Alternating Series Test, we can conclude that the series converges.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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